What OS version do you have?
Do you have anti-virus software enabled? If so, what is it and which version?
Try disabling the anti-virus software and running the installer again.
If the error continues, please provide the FlashInstall.log file saved at C:\Windows\System32\Macromed\Flash. If this is a 64-bit OS, also provide the FlashInstall.log file saved at C:\Windows\SysWOW64\Macromed\Flash. The files will be fairly large, as such you can upload them to cloud.acrobat.com using the instructions at The specified item was not found., or some other file sharing site. Provide the URL to the uploaded files in your reply.